Get Expert Help with Integration Homework - Essential Equations & Solutions

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Homework Statement



http://prikachi.com/images/201/4687201t.gif

Homework Equations



Given in class on material connected with undefined integral

The Attempt at a Solution


Hard for me to grasp that one...
P.S Thanks in advance
 
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Use integration by partial fractions.
 
grindfreak said:
Use integration by partial fractions.
The integrand is not a rational expression, so I don't see how this technique could work.

A better approach, I believe, is to complete the square inside the radical, and then use a trig substitution.
 
Hmmm, good point trig substitution would probably work.
 
I finally done it with a little help from a friend :)
http://prikachi.com/images/946/4687946U.gif
which is arcsin√x +C
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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